Problem of the Week 1005

A Regular Nonregular Problem

Suppose a polygon having 1005 vertices is inscribed in a circle. Suppose further that the polygon is equiangular (the 1005 angles made by three consecutive points are all equal). Is the polygon necessarily regular? That is, must the sides all have the same length?

Source: Indiana College Mathematics Competition 1975, in "A Friendly Mathematics Competition," MAA Problem Books, 2003.

© Copyright 2004 Stan Wagon. Reproduced with permission.